The latest version of Telegram Desktop (0.9.27) doesn't have feature to change the phone number in itself. But there is a way to change the number by using another instance of Telegram. Hope this helps a lot.

The Case

Suppose you have a Telegram account with your old & already inactive phone number. You want to change the old phone number into the new one you've prepared. Your only Telegram is the Telegram Desktop client on your GNU/Linux. You can't/worry to use smartphone version of Telegram, because your old number was already inactive. And you don't find any button/any way in Telegram Desktop to change the number directly.

Preparation

You need an another device to install new Telegram instance. The ideal one is an Android smartphone.

Prepare one new active phone number.

Ensure your Telegram Desktop in GNU/Linux is logged in and active with your old phone number account. This is a must.

1. Another Device

Have another device (i.e. Android smartphone) and install Telegram there. For Android, install Telegram from Google PlayStore. If you don't have it, you probably can borrow it from your friend.

2. Login from Another Device

After installing, using the another device/smartphone, login into your old phone number Telegram account. This will trigger Telegram system to send secret code into your Telegram Desktop running on GNU/Linux. This will also send SMS message containing same secret code into your old phone number (but this old number was already inactive).

3. Enter Secret Code in Another Device

In the Telegram login page in your another device/smartphone, enter the secret code you get from your running Telegram Desktop. Now you can log into Telegram with another device/smartphone. In this phase, you have two devices logged in concurrently: your another device (Telegram Mobile) and your desktop (Telegram Desktop).

4. Change Your Phone Number in Another Device

In another device/smartphone, go to Telegram Settings > tap your phone number > change your old phone number with the new phone number you've prepared. Follow any instruction later until you have successfully changed it. All of your Telegram instances (Mobile & Desktop) will be informed that the number was changed.

Thanks for Telegram Support for guiding me until I can change my phone number.